Answer:

Given two lines, they define a plane only if they are:
parallels non coincident or non coincident intersecting.

Explanation:

Given two lines, they define a plane only if they are:
parallels non coincident or non coincident intersecting. If they are parallels, taking a point in one of them and the support of the other we can define a plane. If they intersect, with the normal to both directions and their intersection point, a plane can also be constructed.

Let #A, B and C# be three noncolinear points, #A, B, C in P#
Note that #A, B and C# define two vectors #vec (AB)# and #vec (AC)# contained in the plane #P#. We know that the cross product of two vectors contained in a plane defines the normal vector of the plane.

Now, we can use an example to illustrate the solution. Assume that the coordinates of the three points are the following:#A(1,2,3), B(-2,1,0)# and #C(0,3,2)#

From the coordinates of the points #A, B# and #C# we can find the vectors #vec (AB)# and #vec (AC)#: